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We establish the existence of a chiral spin liquid (CSL) as the exact groundstate of the Kitaev model on a decorated honeycomb lattice, which is obtainedby replacing each site in the familiar honeycomb lattice with a triangle. TheCSL state spontaneously breaks time reversal symmetry but preserves othersymmetries. There are two topologically distinct CSLs separated by a quantumcritical point. Interestingly, vortex excitations in the topologicallynontrivial (Chern number $\pm 1$) CSL obey non-Abelian statistics.

An exact chiral spin liquid with non-Abelian anyons